### Abstract

It is shown that if G has clique-width k, and a corresponding tree decomposition is known, then a diagonal matrix congruent to A- cI for constants c, where A is the adjacency matrix of the graph G of order n, can be computed in time O(k^{2}n). This allows to quickly tell the number of eigenvalues in a given interval.

Original language | English (US) |
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Title of host publication | LATIN 2018 |

Subtitle of host publication | Theoretical Informatics - 13th Latin American Symposium, Proceedings |

Editors | Miguel A. Mosteiro, Michael A. Bender, Martin Farach-Colton |

Publisher | Springer Verlag |

Pages | 475-489 |

Number of pages | 15 |

ISBN (Print) | 9783319774039 |

DOIs | |

State | Published - Jan 1 2018 |

Event | 13th International Symposium on Latin American Theoretical Informatics, LATIN 2018 - Buenos Aires, Argentina Duration: Apr 16 2018 → Apr 19 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10807 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 13th International Symposium on Latin American Theoretical Informatics, LATIN 2018 |
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Country | Argentina |

City | Buenos Aires |

Period | 4/16/18 → 4/19/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings*(pp. 475-489). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10807 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-77404-6_35

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*LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10807 LNCS, Springer Verlag, pp. 475-489, 13th International Symposium on Latin American Theoretical Informatics, LATIN 2018, Buenos Aires, Argentina, 4/16/18. https://doi.org/10.1007/978-3-319-77404-6_35

**Locating the eigenvalues for graphs of small clique-width.** / Fürer, Martin; Hoppen, Carlos; Jacobs, David P.; Trevisan, Vilmar.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Locating the eigenvalues for graphs of small clique-width

AU - Fürer, Martin

AU - Hoppen, Carlos

AU - Jacobs, David P.

AU - Trevisan, Vilmar

PY - 2018/1/1

Y1 - 2018/1/1

N2 - It is shown that if G has clique-width k, and a corresponding tree decomposition is known, then a diagonal matrix congruent to A- cI for constants c, where A is the adjacency matrix of the graph G of order n, can be computed in time O(k2n). This allows to quickly tell the number of eigenvalues in a given interval.

AB - It is shown that if G has clique-width k, and a corresponding tree decomposition is known, then a diagonal matrix congruent to A- cI for constants c, where A is the adjacency matrix of the graph G of order n, can be computed in time O(k2n). This allows to quickly tell the number of eigenvalues in a given interval.

UR - http://www.scopus.com/inward/record.url?scp=85045392768&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045392768&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-77404-6_35

DO - 10.1007/978-3-319-77404-6_35

M3 - Conference contribution

AN - SCOPUS:85045392768

SN - 9783319774039

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 475

EP - 489

BT - LATIN 2018

A2 - Mosteiro, Miguel A.

A2 - Bender, Michael A.

A2 - Farach-Colton, Martin

PB - Springer Verlag

ER -